Nematic liquid crystal waveguide arrays

OPTO-ELECTRONICS REVIEW 13(2), 107–112
7 th International Workshop on Nonlinear Optics Applications
Nematic liquid crystal waveguide arrays
K.A. BRZD¥KIEWICZ *1 , M.A. KARPIERZ 1 , A. FRATALOCCHI 2 , G. ASSANTO 2 ,
and E. NOWINOWSKI-KRUSZELNICKI 3
1 Faculty of Physics, Warsaw University of Technology, 75 Koszykowa Str., 00–662 Warsaw, Poland
2 NooEL-Nonlinear Optics and Optoelectronics Laboratory, University “Roma Tre”,
Via della Vasca Navale 84, 00–146 Rome, Italy
3 Institute of Applied Physics, Military University of Technology, 2 Kaliskiego Str., 00–908 Warsaw, Poland
We investigate linear and nonlinear light propagation in a voltage-tunable array of waveguide channels in undoped nematic
liquid crystals. This novel geometry, based on a photonic structure with a periodic modulation of refractive index controlled
by an electric field, offers a wealth of possibilities for the study of discrete optical phenomena. The structure, in conjunction
with a giant, non-resonant and voltage-dependent reorientational nonlinearity, allows us to drive the system from bulk diffraction
to discrete propagation. Theoretical and experimental investigations, carried out with near infrared light wavelength
and powers of a few milliWatts, show the possibility of transverse light localization, resulting in discrete spatial solitons.
Such array, with its voltage- and light-adjustable guided-wave confinement and coupling, exhibits potentials for the realization
of multifunctional routers and all-optical signal processors with nematic liquid crystals.
Keywords: nonlinear optics, solitons, self-action effects, optical nonlinearity in liquid crystals, discrete diffraction.
1. Introduction
Linear and nonlinear effects in discrete systems such as
photonic structures with a periodic modulation of the refractive
index have became the subject of intensive investigations.
Particular attention has been devoted to the generation
of discrete solitons [1,2] which are excellent candidates
for novel all-optical switching devices and networks
[3–6]. Similarly to continuous systems, stable spatial
solitons can be formed in discrete structures when self focusing
is strong enough to balance discrete diffraction.
Moreover, discrete solitons can be viewed as due to a nonlinear
response which detunes a waveguide from the neighbouring
ones. General properties of discrete optical solitons
were first described by Christodoulides et al. referring to a
cubic Kerr nonlinearity [7] and later studied with reference
to other nonlinear materials, including photorefractive and
parametric crystals [1,8]. To the date, they were observed
experimentally in AlGaAs [9–12], in silica [13,14], in
SBN-crystals [15,16], in Lithium Niobate [17], and recently
also in nematic liquid crystals (NLC) [18]. The latter
were proven to be very promising for nonlinear optics
[19–21]. Their inexpensive and consolidated technology,
huge birefringence, giant reorientational nonlinearity and
low power requirements, have allowed us demonstrating
that spatial solitons can be effectively generated at mW
power levels, in bulk as well as in planar waveguide configurations,
with propagation distances of a few millimeters
[20]. Moreover, the large electro-optic response of NLC allows
for creation of flexible and voltage-tunable architectures,
useful for the study of discrete phenomena. In this
communication, we illustrate a one-dimensional periodic
photonic structure with refractive index contrast controlled
by an external electric field. We present experimental and
theoretical analyses of both linear and nonlinear discrete
propagation of infrared-light in arrays of identical
weakly-coupled waveguides in undoped nematic crystals,
paying particular attention to the choice of geometric parameters.
A sketch of the device is drawn in Fig. 1. A few-micron
thick layer of PCB (4-cyano-4'-n-pentylbiphenyl) nematic
liquid crystal is sandwiched between two glass plates,
forming a planar waveguide in the absence of an applied
voltage. The anchoring conditions at the top and bottom
glass surfaces determine the planar alignment of the molecules
in the z-direction. To introduce a spatially periodic
refractive modulation inside of NLC layer and to obtain a
voltage-adjustable response, a set of regularly-spaced,
transparent indium-tin-oxide (ITO) electrodes (as thin as
50 nm) is placed on the top surface to apply a reorientational
bias across the cell. The comb-shape of this electrode
(with equal finger widths and spacing) allows us the
formation of identical channels and provides confinement
in the transverse x-y plane. In our samples, the electrode set
had the periods ranging from 4 to 8 µm depending on the
cell thickness.
* e-mail: kasia@if.pw.edu.pl
Opto-Electron. Rev., 13, no. 2, 2005 K.A. Brzd¹kiewicz 107

Nematic liquid crystal waveguide arrays
Fig. 1. Sketch of the liquid crystal waveguide array. The period of
the electrode distribution L varies from 4 to 8 µm and the cell
thickness d from 3 to 7 µm (depending on the cell).
2. Numerical results
The application of an appropriate voltage causes the reorientation
of the NLC molecules which, as a result of free-
-energy minimization, tend to align parallel to the direction
of the electric field. The angular molecular distribution can
be theoretically calculated from the Euler-Lagrange equation
describing reorientation through an applied bias [21].
The numerical results shown in this communication were
obtained for the liquid crystal PCB, with low-frequency
anisotropy De if = 115 . . Owing to a new arrangement of the
orientation angle, a periodic spatial modulation of the refractive
index occurs. Figure 2 shows an example of refractive
index distribution (for x-polarized light) obtained in
the 5-µm-thick sample and for electrode period of 6 µm.
Figure 2(b) presents numerical results of refractive index
distribution in the middle of the NLC layer (i.e., for x =0)
and three different values of bias. As one can see, the refractive
index increases mainly in the regions under the
electrodes and thereby the channel waveguides are well defined
through lateral confinement. In general, the higher refractive
index is obtained for a higher bias, and better light
guiding is expected. In this case, the coupling length, defined
as the propagation distance at which whole energy
goes from one waveguide to the neighbouring ones [23],
gets longer.
Numerical simulations of light propagating in the NLC
layer were carried out with BPM injecting a TM-polarized
Gaussian beam. Additionally, in each propagation step the
molecular orientation distribution was recalculated based
on minimization of the total free-energy of the liquid crystal
under the influence of both the low-frequency (bias) and
the optical electric field [21]. The refractive indices characteristic
of PCB are n 0 = 1.52 and n e = 1.69 at a wavelength
of 1064 nm. Figure 3 displays light propagation in the linear
(low input optical power) regime. In this case, the electric
bias plays a crucial role in the reorientation process,
leading to the periodic modulation of a refractive index, as
shown in Fig. 2. While standard diffraction (in the homogenous
medium) takes place in the transverse y-z plane in the
absence of bias, discrete diffraction [1,2,22] sets-in and can
be tuned in strength as the voltage increases and the array
is formed. As a consequence of discrete diffraction, energy
redistributes among the guiding channels, as clearly visible
in Figs. 3(b)–3(e) showing the cross-sections in x = 0 and
beam transverse profiles in the x-y plane along propagation.
In the analysed geometry, the optimisation of such parameters
as the optical properties (especially birefringence)
of NLC, the NLC layer thickness, the electrode spacing and
width, allows us to obtain properly coupled and well defined
waveguides. Moreover, the magnitude of discrete diffraction
can be easily tuned by controlling the voltage.
Figure 4 shows how the coupling between channels and
the resulting discrete diffraction changes with the applied
voltage. An increase in bias reduces angular divergence of
the beam; light is more confined within the core region of
the channels, and the coupling length increases. As intuitive,
by increasing the bias it is possible to progressively
Fig. 2. Spatial distribution of the refractive index for light linearly polarized along x, NLC layer 5-µm thick and electrode width and spacing
of 3 µm. Three-dimensional map for the bias V = 1.35 V (a), refractive index in the middle of the NLC cell (i.e., for x = 0) for three different
applied voltages (b).
108 Opto-Electron. Rev., 13, no. 2, 2005 © 2005 COSiW SEP, Warsaw

7 th International Workshop on Nonlinear Optics Applications
Fig. 3. Numerical results for a low-power Gaussian optical input of waist 2 µm and wavelength 1064 nm, for a 5-µm-thick NLC-cell,
electrode period of 6 µm and applied voltage V = 1.35 V. Discrete diffraction for the beam launched into one input waveguide (a). Beam
transverse profiles (for x = 0) (b) and (c), spatial distribution of light intensity (d) and (e) after 1- and 2-mm propagation distances,
respectively.
reduce light transfer between channels. By using a proper
bias the difference between refractive indices in each channel
and in the gaps between the finger electrodes can be
maximized. However, the saturating character of this reorientation
process causes an excessive voltage to flatten the
index profile and thereby weaken the spatial definition of
each channel. The non local response of NLC, in fact, is
such that an electric field increases the index not only under
electrodes but also between them. For high enough applied
voltages, the NLC elastic response mediates reorientation
in the regions between neighbouring waveguides,
thereby reducing the refractive index modulation. This is
also visible in Fig. 5(a) where, for a fixed cell thickness,
the coupling length first increases with applied voltage until
saturation and non locality makes it decrease again.
Figure 5 shows how discrete diffraction can be modified
by varying the sample geometry. By reducing the
thickness of the NLC layer it is possible to obtain better defined
waveguides, i.e., an increased coupling length,
Fig. 5(b). Figure 5(c) shows how the light beam injected in
a 2.5-µm-thick sample for low bias (1.2 V) is confined
within 3 channels after 1-mm propagation. Conversely, for
thicker NLC layers, the change in coupling length versus
voltage is negligible and discrete diffraction is hardly affected.
As expected, the coupling length can be also reduced by
decreasing the electrode periodicity. However, a close
proximity of the stripe electrodes reduces the coupling
length dependence with bias. For example, in a 5-µm-thick
sample with 4-µm electrode period, by varying the voltage
from 1.1 to 1.9 V, the change in coupling distance is
around 60 µm. The analyses demonstrate that, in the process
of sample designing, it is important to find the optimum
ratio between electrode width and sample thickness
in order to obtain a well tunable structure for suitable values
of the applied voltage.
Fig. 4. Linear coupling between channels and its dependence on applied voltage for NLC thickness of 5 µm and electrode period of 6 µm.
The optical intensity distribution is colour-inverted (i.e., darker corresponds to a higher intensity) and evaluated after 1 mm propagation.
Opto-Electron. Rev., 13, no. 2, 2005 K.A. Brzd¹kiewicz 109

Nematic liquid crystal waveguide arrays
Fig. 5. Linear coupling between channels versus NLC thickness. Dependence of a coupling length on applied voltage for three cell
thicknesses d (a). Coupling length versus NLC thickness at a voltage V = 1.2 V (b). Spatial intensity distribution calculated after 1 mm
propagation and V = 1.2 V for different values of NLC thickness d (c).
Going from the linear to the nonlinear regime, as the
power of the propagating beam increases, the refractive index
of the excited waveguides is modified by the nonlinearity,
and discrete diffraction can be effectively counteracted
by the power-induced detuning of the launch channel.
As shown in Fig. 6, as the light power gets higher, the
beam narrows in space. Finally, when the input beam is intense
enough, nonlinearity completely balances diffraction
and light propagates (transversely) localized in a limited region
of the array or, for high enough excitations, in a single
channel. Such a beam, which propagates maintaining an invariant
transverse profile, is called discrete spatial soliton
[1,2,18,22]. It is possible to consider either partially localized
or “wide” solitons with energy in a few channels, or
totally localized “narrow” solitons, with energy essentially
confined in the input waveguide. It is worth to underline
that, due to light confinement, discrete systems require less
power for solitons than comparable slab waveguide or bulk
media.
Fig. 6. Beam distribution versus input beam power calculated for V
= 1.35 V after 1-mm propagation. Discrete diffraction is limited
and discrete spatial solitons are generated due to increase in input
light power.
3. Experimental results
We performed experiments in NLC cell of a thickness of
5–6 µm and with an array period of 6 µm. The beam from a
Nd:YAG laser (l = 1064 nm) was focused to a diameter of
approximately 4 µm at the entrance of the sample. The
beam evolution in the NLC cell was observed through a
CCD camera detecting the photons scattered above the cell.
Photographs were taken at various biases, as shown in
Fig. 7. The pictures show the change in discrete beam propagation
for a fixed input power of 5 mW and a propagation
distance of 1 mm. As one can see, by increasing the applied
voltage the coupling length becomes longer and beam spatial
localization is enhanced. For low voltages [Figs. 7(a)
and 7(b)], the beam is guided in a few channels, whereas
V = 1.45 V it essentially propagates in just one of them.
As predicted theoretically, however, spatial light localization
can be also obtained by increasing the beam power,
leading to discrete soliton generation.
Figure 8 shows the experimental photographs of light
propagation depending on optical power in the structure.
When no voltage is applied, the beam diffracts in the y-z
plane, progressively reducing its intensity and becoming
hardly visible after a few Rayleigh ranges, see Fig. 8(a).
Figure 8(b) shows discrete diffraction of the excitation injected
into a single channel for a bias V = 1.1 V, large
enough to create an array of well-defined channels. In
z = 1.4 mm, the input has spread over 13 adjacent waveguides.
Compared to standard diffraction in a homogeneous
1D geometry [planar waveguide, Fig. 8(a)], discrete
diffraction [Fig. 8(b)] gives rise to the smaller divergence.
Figures 8(c)–8(e) present the successive changes of the
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7 th International Workshop on Nonlinear Optics Applications
4. Conclusions
Fig. 7. Experimental results showing a 5-mW Nd:YAG beam after
1-mm propagation for three different applied voltages.
character of discrete propagation obtained due to increment
of the beam evolution versus optical power. As expected,
a high excitation mismatches the input waveguide, resulting
in a “narrow” discrete soliton [Fig. 8(e)]. Figures
8(f)–8(i) show the corresponding beam transverse profiles
in z = 1.4 mm.
In conclusions, we have presented nonlinear waveguide
arrays in undoped nematics. The investigated geometry
takes advantage of both the electro-optic and all-optical
response of liquid crystals in a planar arrangement, offering
considerable flexibility both in the linear and nonlinear
regimes by voltage tuning the relevant parameters.
The giant nonlinear response characteristic of molecular
reorientation in such medium, allows for observation of
discrete spatial solitons at mW levels, paving the way to
multifunctional routers and signal processors in liquid
crystals. The theoretical predictions are in excellent
agreement with the experimental results, and further
work is underway to enlighten a variety of additional fascinating
phenomena including gap solitons and discrete
breathers.
Acknowledgments
This work was partially supported by the State Committee
for Scientific Research under grant No. 4 T11B 058 25.
Fig. 8. Linear propagation (standard diffraction) of the beam in the homogenous planar waveguide (i.e., at zero voltage) (a). Light
propagation (for voltage of 1.1 V) for different input powers of the beam launched into one channel (b–e). Acquired transverse profiles
(solid line) in z = 1.4 mm, corresponding to the cases (b–e) (f–i). The dashed-line graphs are calculated profiles matching the experimental
conditions.
Opto-Electron. Rev., 13, no. 2, 2005 K.A. Brzd¹kiewicz 111

Nematic liquid crystal waveguide arrays
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